积极 AI Logo 积极 AI

弧度、数轴与单位圆

弧度、数轴与单位圆
几何画板及绘图内容加载中，请稍等……
2015-01-10 01:27
三角函数解析几何几何作图
①本范例演示了数轴上的点与单位圆上点的一一对应关系；②涉及的核心数学概念包括弧度制、三角函数、单位圆、数轴；③作图要点——使用了Vector（向量）、Text（文本）、Length（长度）、Intersect（交点）、Point（点）、Circle（圆）、If（条件）、Rotate（旋转）、Tangent（切线）、Ray（射线）、UnitVector（单位向量）、Sequence（序列）、CircleArc（圆弧）、Take（取值）、Segment（线段）、Textfield（文本框）、CurveCartesian（笛卡尔曲线）等GeoGebra命令/对象；④适合高中数学教学，用于帮助学生理解三角函数与单位圆的联系，适合学习解析几何和三角函数的学生。

GeoGebra 命令及参数

  1. Vector((0, 0), (1, 0)) → u_1
  2. Text(A50) → B50
  3. Text(A49) → B49
  4. Text(A48) → B48
  5. Text(A47) → B47
  6. Text(A46) → B46
  7. Text(A45) → B45
  8. Text(A44) → B44
  9. Text(A43) → B43
  10. Text(A42) → B42
  11. Text(A41) → B41
  12. Text(A40) → B40
  13. Text(A39) → B39
  14. Text(A38) → B38
  15. Text(A37) → B37
  16. Text(A36) → B36
  17. Text(A35) → B35
  18. Text(A34) → B34
  19. Text(A33) → B33
  20. Text(A32) → B32
  21. Text(A31) → B31
  22. Text(A30) → B30
  23. Text(A29) → B29
  24. Text(A28) → B28
  25. Text(A27) → B27
  26. Text(A26) → B26
  27. Text(A25) → B25
  28. Text(A24) → B24
  29. Text(A23) → B23
  30. Text(A22) → B22
  31. Text(A21) → B21
  32. Text(A20) → B20
  33. Text(A19) → B19
  34. Text(A18) → B18
  35. Text(A17) → B17
  36. Text(A16) → B16
  37. Text(A15) → B15
  38. Text(A14) → B14
  39. Text(A13) → B13
  40. Text(A12) → B12
  41. Text(A11) → B11
  42. Text(A10) → B10
  43. Text(A9) → B9
  44. Text(A8) → B8
  45. Text(A7) → B7
  46. Text(A6) → B6
  47. Text(A5) → B5
  48. Text(A4) → B4
  49. Text(A3) → B3
  50. Text(A2) → B2
  51. Text(A1) → B1
  52. Length(numb) → l
  53. Intersect(xAxis, yAxis) → B
  54. Point(xAxis) → O
  55. Circle(O, B) → c
  56. If(WrapPositive ≥ pi / 2, WrapPositive - pi / 2, 0) → f
  57. Rotate(M, f, O) → M'
  58. Tangent(M', c) → b,
  59. Point(b) → D
  60. Ray(M', D) → e
  61. UnitVector(e) → u
  62. Point(xAxis) → C
  63. If(WrapPositive ≤ pi / 2, WrapPositive, 1.5707963267948966) → α
  64. Rotate(B, α, B) → B'
  65. Rotate(C, α, B) → C'
  66. Ray(B', C') → a'
  67. Rotate(B', f, B) → B''
  68. Sequence(Point[M', Vector[If[(k * st) - f ≥ 0, Vector[(u * ((k * st) - f))]]]], k, 0, l) → list1
  69. CircleArc(O, M, M') → d
  70. If(f ≟ 0, RemoveUndefined[list1], Append[(0, 0), RemoveUndefined[list1]]) → ptsR
  71. Sequence((cos(k) - 1, sin(k)), k, 0, f, st) → ptsC
  72. Circle(O, B) → g
  73. UnitVector(a') → v
  74. Sequence(Point[M, Vector[((k * st) * v)]], k, 0, l) → list2
  75. Sequence(Text[Element[numb, k + W + 1], Element[ptsR, k + 1], true, true], k, 0, l - 1) → numR
  76. Take(numR, 2) → NewPtsR
  77. Point(c) → A
  78. Segment(O, A) → ii
  79. Rotate(A, WrapPositive) → A'
  80. If(WrapPositive > pi / 2, Segment[Rotate[O, WrapPositive - pi / 2, O], Rotate[A, WrapPositive - pi / 2, O]]) → j
  81. Textfield(st) → inputBox1
  82. Rotate(A, 6.2831, O) → A'_1
  83. Sequence(Text[Element[numb, k], Element[list2, k], true, true], k, 1, l) → nmbX
  84. Take(Sequence[Text[Element[numb, k], Element[ptsC, k], true, true], k, 1, l], 2) → numC
  85. Text(C1) → D1
  86. Text(C2) → D2
  87. Text(C3) → D3
  88. Text(C4) → D4
  89. Text(C5) → D5
  90. Text(C6) → D6
  91. Text(C7) → D7
  92. Text(C8) → D8
  93. Text(C9) → D9
  94. Text(C10) → D10
  95. Text(C11) → D11
  96. Text(C12) → D12
  97. Text(C13) → D13
  98. Text(C14) → D14
  99. Text(C15) → D15
  100. Text(C16) → D16
  101. Text(C17) → D17
  102. Text(C18) → D18
  103. Text(C19) → D19
  104. Text(C20) → D20
  105. Text(C21) → D21
  106. Text(C22) → D22
  107. Text(C23) → D23
  108. Text(C24) → D24
  109. Text(C25) → D25
  110. Text(C26) → D26
  111. Text(C27) → D27
  112. Text(C28) → D28
  113. Text(C29) → D29
  114. Text(C30) → D30
  115. Text(C31) → D31
  116. Text(C32) → D32
  117. Text(C33) → D33
  118. Text(C34) → D34
  119. Text(C35) → D35
  120. Text(C36) → D36
  121. Text(C37) → D37
  122. Text(C38) → D38
  123. Text(C39) → D39
  124. Text(C40) → D40
  125. Text(C41) → D41
  126. Text(C42) → D42
  127. Text(C43) → D43
  128. Text(C44) → D44
  129. Text(C45) → D45
  130. Text(C46) → D46
  131. Text(C47) → D47
  132. Text(C48) → D48
  133. Text(C49) → D49
  134. Text(C50) → D50
  135. If(WrapNegative ≤ pi / 2, WrapNegative, 1.5707963267948966) → ε
  136. Ray(A, O) → k
  137. If(WrapNegative > pi / 2 + 0.5, WrapNegative - pi / 2 - 0.5, 0) → m
  138. Rotate(A, ε, M) → A'_2
  139. Rotate(O, ε, M) → O'
  140. Ray(A'_2, O') → k'
  141. UnitVector(k') → w
  142. Sequence(Point[M, Vector[((i * st) * w)]], i, 0, l) → ptsXN
  143. Rotate(M, (-m), O) → MM
  144. Tangent(MM, c) → n,
  145. Point(n) → F
  146. Ray(MM, F) → p
  147. UnitVector(p) → q
  148. Sequence(Point[MM, Vector[If[(k * st) - m ≥ 0, Vector[(q * ((k * st) - m))]]]], k, 0, l) → ptsRN
  149. If(m ≟ 0, RemoveUndefined[ptsRN], Append[(0, 0), RemoveUndefined[ptsRN]]) → ptsRN_1
  150. Take(Sequence[Text[Element[numbN, k + WN + 1], Element[ptsRN_1, k + 1], true, true], k, 0, l - 1], 2) → numRN
  151. CircleArc(O, MM, M) → r
  152. Sequence((cos(k) - 1, (-sin(k))), k, 0, m, st) → ptsCN
  153. Take(Sequence[Text[Element[numbN, k], Element[ptsCN, k], true, true], k, 1, l], 2) → numCN
  154. Sequence(Text[Element[numbN, k], Element[ptsXN, k], true, true], k, 1, l) → numXN
  155. If(WrapPositive > pi / 2, Segment[Rotate[O, WrapPositive - pi / 2, O], Rotate[A, WrapPositive - pi / 2, O]]) → s
  156. Circle(O, B) → c_1
  157. Segment(O, A) → a_1
  158. If(a ≟ false ∧ h ≟ false, true, false) → start
  159. Sequence(Point[M, Vector[((i * st) * u_1)]], i, 0, l) → ptsXP
  160. Ray(M, C) → b_1
  161. Sequence(Text[Element[numb, k], Element[ptsXP, k], true, true], k, 1, l) → list3
  162. Ray(A, O) → d_1
  163. Vector((0, 0), (-1, 0)) → v_1
  164. Sequence(Point[M, Vector[((i * st) * v_1)]], i, 0, l) → ptsXNS
  165. Sequence(Text[Element[numbN, k], Element[ptsXNS, k], true, true], k, 1, l) → list4
  166. CurveCartesian(((0.2 / 16 * (t + (6 * pi))) * cos(t + (6 * pi))) - 1, ((0.2 / 16 * (t + (6 * pi))) * sin(t + (6 * pi))), t, 0, WrapPositive - pi / 2) → o
  167. Tangent(End, o) → e_1
  168. UnitVector(e_1) → w_1
  169. Vector(End, Point[End, Vector[(0.12 * w_1)]]) → f_1
  170. CurveCartesian(((0.2 / 16 * (t + (6 * pi))) * cos(t + (6 * pi))) - 1, ((-0.2 / 16 * (t + (6 * pi))) * sin(t + (6 * pi))), t, 0, WrapNegative - pi / 2 - 0.5) → j_1
  171. Tangent(K, j_1) → i
  172. UnitVector(i) → g_1
  173. Vector(K, Point[K, Vector[(0.12 * g_1)]]) → h_1
  174. If(WrapNegative > pi / 2 + 0.5, Segment[Rotate[O, (-WrapNegative) + pi / 2 + 0.5, O], Rotate[A, (-WrapNegative) + pi / 2 + 0.5, O]]) → t

AI 绘图提示语参考

画一条水平数轴，并在其上标出从-2π到2π的多个等分点，每个点旁边标注对应的弧度值。以原点为中心画一个单位圆，从原点出发画一条与数轴重合的射线。在射线上从原点开始每隔一定距离标出单位长度的点，并将这些点与单位圆上的对应点用线段连接。在单位圆上标出角度为0°、30°、45°、60°、90°等特殊角度的点，并标注这些点的坐标。
以上提示语为根据原始绘图命令整理而来，仅供参考。